Heat transfer and cost are two important parameters of designing a heat exchanger. Mostly, in engineering affairs the goals of interest for optimization are in conflict with each other. In the other hand, by making progress in one parameter, an undesirable factor appears. There is the same problem in heat exchangers. By increasing the heat transfer, heat area, cost and pressure drop increase. Thus, instead of one solution, there are several solutions. In this study for computing the heat transfer and pressure drop, Bell Delaware method is used. Lots of usual optimization methods for extracting the solutions are not efficient. At current research an efficient method is presented based on group particle algorithm and genetic, according to multi goaled function for optimizing of these exchangers. In addition, in optimization by two algorithms, two tube arrangement modes were considered, both square and triangular arrangement, which, At the end of this research, the results obtained from two algorithms for different modes and other research results have been compared.